A Mathematical Model of the Chemostat with a General Class of Functions Describing Nutrient Uptake

A model of the chemostat involving n microorganisms competing for a single essential, growth-limiting substrate is considered. Instead of assuming the familiar Michaelis-Menten kinetics for nutrient uptake, a general class of functions is used which includes all monotone increasing uptake functions, but which also allows uptake functions that describe inhibition by the substrate at high concentrations. The qualitative behaviour of this generalized model is determined analytically. It is shown that the behaviour depends intimately upon certain parameters. Provided that all the parameters are distinct (which is a biologically reaonable assumption), at most one competitor survives. The substrate and the surviving competitor (if one exists), approach limiting values. Thus there is competitive exclusion. However, unlike the standard model, in certain cases the outcome is initial condition dependent.